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NTU Management Review Vol. 36 No. 1 Apr. 2026

sufficient condition of a small degree of ambiguity aversion. Specifically, when the
*
ambiguity exists for losses below D , the smooth ambiguity aversion model implies that
a straight deductible remains optimal under a small degree of ambiguity aversion. Our
result is consistent with the observational equivalence between the effects of changes in

the individual’s beliefs and ambiguity aversion on optimal insurance coverage noted by
Gollier (2011, 2014).
We illustrate Proposition 3 with a numerical example. In Figure 2, Panel A

presents all the cumulative loss distribution functions, and Panel B presents the optimal
indemnity in the presence of ambiguity. Consider a discrete loss x that takes a value
in the set {0,1,2,3,4,5} and an initial wealth w = 6. The individual’s risk aversion and
ambiguity aversion are measured by the constant absolute risk aversion function (CARA)
√z
with the CARA coefficient γ = 0.5, as assumed by Gollier (2014) (Proposition 5),
u(z) =
2
and α = 0.56, as estimated by Dimmock, Kouwenberg, Mitchell, and Peijnenburg (2015)
via survey. The premium loading factor is τ = 0.2. In the absence of ambiguity, the loss
distribution (the dark dotted line in Panel A) is G(x;π ), with the set of cumulative loss
*
probabilities {0.1667,0.3334,0.5001,0.6668,0.8335,1}. As expected, the optimal insurance
*
contract is a straight deductible, with a deductible level of D = 3.42 (the dark dotted line
in Panel B).
In the presence of ambiguity, the loss distributions considered are G(x;π ) and
_ F
G(x;¯π ), represented in Panel A by the dark dashed and solid lines, respectively. For
F
G(x;π ), the set of cumulative loss probabilities is {0.0500,0.1734,0.3094,0.4194,0.70
_ F
94,1}. For G(x;¯π ), the set of cumulative loss probabilities is {0.2834,0.4934,0.6908,
F
0.9142,0.9576,1}. Under these loss distributions, Assumptions 1–3 hold. As predicted by

Proposition 3, the optimal insurance contract is also a straight deductible, albeit with a
lower deductible level of D = 3.11 in this example (the dark solid line in Panel B).
*
F
As a counterexample, the light dashed and solid lines in Panel A show the loss
distributions G(x;π ) and G(x;¯π ), respectively. Their sets of cumulative loss probabilities
K
_ K
are {0,0.0001,0.4901,0.6401,0.7506,1} and {0.0001,0.9914,0.9964,0.9984,0.9996,1},
respectively. The size of the set, Δ , with boundaries G(x;π ) and G(x;¯π ), is much larger
_ K
K
K
than Δ . Moreover, Assumption 2 does not hold in this case. The optimal contract (the light
F
dashed line in Panel B) is not a straight deductible.
The following comparative statics of an ambiguity increase are based on Proposition

15